I’m going to go out on a limb and say that every game has a tone, regardless of what kind of game it is. Which was includes abstracts, RPGs and video games.
And while tone is an essential part of theme, tone is not theme. Every element of a game, theme and components and the rules and the language of the rules contribute to overall character of a game.
Go clearly has a tone even though it has no theme and consists of a wooden board and two colors of stones. The austerity of its rules and its components let you understand what the experience of Go is going to be like. Quiet and calm until someone grabs the board and starts swinging. Go also has the weight of history behind it, which becomes another element of tone.
While I don’t think there has ever been a time when tone hasn’t been an important part of game design and game experience (I refuse to believe the unnamed monk or scholar who developed Rithmomachy didn’t want it to be more erudite than human endurance could handle), I think it has become more laser-focused as modern gaming has developed. As more games are developed at a greater and greater amount, every element ought to be seriously considered.
What got me seriously thinking down this path was the now venerable-by-modern-standards Guillotine, the jovial, silly game of competitive decapitation. With just a little tweaking and no rule changes, it could easily go to much darker black comedy or straight up horror. The light-heartedness was not a happy mistake but intentional.
Guillotine is a pretty heavy-handed example. I have a pretty good feeling if you did a more exhaustive study than I’m up for, you’d see a lot more subtle examples. You could probably write a dissertation about tone and Kickstarter projects, if that hasn’t already been done.
Theme is what a game is about. Mechanics are how you do stuff. Maybe one way to describe tone is what a game is trying to say.